本文推衍混合分層(Layerwise, LW)高階剪切變形理論(Higher-Order Shear Deformation Theory, HSDT)的強型式與弱型式數學方程式，進行在各種邊界條件束制下，功能性梯度(Functionally Graded, FG)梁承受熱彈載重下的靜力分析。文中假設FG梁的材料性質與厚度方向上各成分材料的體積比率相關，並使用二相材料混合法則(The Rule of Mixtures)計算其有效材料參數。
數值範例結果顯示，混合LW HSDT 在熱彈耦合分析中的解與文獻中提供的精確解非常吻合。文中亦討論FG梁在各種不同參數下其熱彈耦合分析的結果，包括長寬比、材料體積組成比率和不同的邊界條件。

The strong and weak formulations of a mixed layer-wise (LW) higher-order shear deformation theory (HSDT) are developed for the static analysis of functionally graded (FG) beams under various boundary conditions subjected to thermo-mechanical loads. The material properties of the FG beam are assumed to obey a power-law distribution of the volume fractions of the constituents through the thickness of the FG beam, for which the effective material properties are estimated using the rule of mixtures, or it is directly assumed that the effective material properties of the FG beam obey an exponential function distribution along the thickness direction of the beam. The results shown in the numerical examples indicate that the mixed LW HSDT solutions for elastic and thermal field variables are in excellent agreement with the accurate solutions available in the literature. A parametric study related to various effects on the coupled thermo-mechanical behavior of FG beams is carried out, including the aspect ratio, the material-property gradient index, and different boundary conditions.

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